An ideal gas undergoes isothermal expansion at constant pressure . During the process.

Options

A. Enthalpy remains constant but entropy increases
B. Enthalpy decreases but entropy increases
C. Enthalpy increases but entropy decreases
D. Both enthalpy and entropy remain constant

Answer

To solve the problem regarding the isothermal expansion of an ideal gas at constant pressure, we can break it down into the following steps:

### Step 1: Understand the Conditions
The problem states that the gas undergoes isothermal expansion at constant pressure. Isothermal means that the temperature remains constant throughout the process.

**Hint:** Remember that isothermal processes imply that the internal energy of an ideal gas remains constant, as it depends only on temperature.

### Step 2: Analyze the Expansion
During the expansion, the volume of the gas increases. Since the gas is expanding, the randomness or disorder of the gas molecules increases. This increase in randomness is associated with an increase in entropy (ΔS).

**Hint:** Entropy is a measure of disorder; more volume means more possible arrangements for the gas molecules.

### Step 3: Calculate the Change in Entropy
For an ideal gas undergoing isothermal expansion, the change in entropy can be calculated using the formula:
\[ \Delta S = nR \ln\left(\frac{V_f}{V_i}\right) \]
where \( n \) is the number of moles, \( R \) is the universal gas constant, \( V_f \) is the final volume, and \( V_i \) is the initial volume.

**Hint:** The logarithmic function indicates that as the volume increases, the entropy change will also increase.

### Step 4: Consider the Enthalpy Change
In an isothermal process for an ideal gas, the change in enthalpy (ΔH) can be evaluated. Since the temperature is constant and there is no chemical reaction occurring, the change in enthalpy is given by:
\[ \Delta H = nC_p \Delta T \]
Since ΔT = 0 (temperature is constant), we find that:
\[ \Delta H = 0 \]

**Hint:** Enthalpy change is related to temperature change; if temperature does not change, enthalpy change is zero.

### Step 5: Conclusion
In summary, during the isothermal expansion of an ideal gas at constant pressure:
- The entropy of the gas increases due to the increase in volume and randomness.
- The enthalpy change remains zero because there is no temperature change.

**Final Answer:** The entropy increases, and the enthalpy change is zero.